Electron–Phonon Coupling in Two-Dimensional Superconductors: Doped Graphene and Phosphorene

Ab initio Eliashberg Theory: Making Genuine Predictions of Superconducting Features

“…Phosphorene is a small gap semiconductor that, upon Li deposition it was predicted to become metallic and superconducting. 87,112,113) In this work we consider Li doping on both faces of the monolayer, a configuration that is likely more difficult to realise experimentally. However it to achieve a higher level of doping and consequently larger critical temperatures.…”

Direct evaluation of the isotope effect within the framework of density functional theory for superconductors

“…The implementation of the method allowed the ab initio calculation of many properties of real superconductors [15,[24][25][26][27][28][29][30] under different conditions [21,[31][32][33][34], and several predictions [35][36][37][38][39][40][41][42]. Among the others, the predicted isotope coefficients for simple metals [15,43], allowed to highlight the origin of reduced isotope effect, underlining the need of a consistent treatment of electron-phonon and renor malized Coulomb electron-electron interaction which ultimately depends on the phonon frequency range.…”

“…Appendix D. Derivative of the deformation potentialSubstituting (C.2) and (B.5) in(42), we obtain∂V λq ∂M α = µ − Z α 2M α Ω λq 2M α Ω λq Ω λq − 1 2 µ1 ζ λq αµ1 * ζ λq αµ1 Ω λq ζ λq αµ Ṽαµ;q (r) α Ω λq λ =λ (Ω 2 λq + Ω 2 λ q ) µ1 ζ λ q αµ1 * ζ λq αµ1 Ω 2 λ q − Ω 2 λq ζ λ q α µ Ṽα µ;q (r) with respect to ΩWe consider again I(ξ 1 , ξ 2 , Ω):∂A ∂Ω = −β A (1 + n β (Ω)) (E.1) ∂B 1 ∂Ω = e βξ1 1 − e −β(ξ1−ξ2−Ω) (ξ 1 − ξ 2 − Ω) 2 − βe −β (ξ1−ξ2−Ω) ξ 1 − ξ 2 − Ω (E.2) ∂B 2 ∂Ω = −e βξ2 1 − e β(ξ1−ξ2+Ω) (ξ 1 − ξ 2 + Ω) 2 + β e β(ξ1−ξ2+Ω) ξ 1 − ξ 2 + Ω (E.3) ∂I ∂Ω = −β (1 + n β (Ω)) I + A e βξ1 1 − e −β(ξ1−ξ2−Ω) (ξ 1 − ξ 2 − Ω) 2 − βe −β (ξ1−ξ2−Ω) ξ 1 − ξ 2 − Ω + e βξ2 1 − e β(ξ1−ξ2+Ω) (ξ 1 − ξ 2 + Ω) 2 + β e β(ξ1−ξ2+Ω) ξ 1 − ξ 2 + Ω…”

Multi-reward Reinforcement Learning Based Bond-Order Potential to Study Strain-Assisted Phase Transitions in Phosphorene

“…Moreover, heterostructures that comprise graphene/phosphorene stacking have resulted in a much wider band gap ranging from 0.004 to 4.26 eV . The α-P and β-P polymorphs have been explored in the areas of chemical catalysis, detectors, and photocatalytic reactions. , Given the wide variation in the polymorph properties of 2D phosphereneblack is semiconducting, whereas blue can be metallicthere has been a lot of effort focused on engineering the phase transformation to exercise better control over phenomena such as electron–phonon coupling enhancement, superconductivity, semiconductor to metal transition, band gap modification, and direct–indirect band gap transition . Strain engineering or applications of pressure represents one of the viable routes to modify the structure and thereby the properties of 2D phosphorene …”